FACTORS AFFECTInG VARIAnCE AnD BIAS OF nOn-nUCLEAR DEnSITY GAUGES FOR POROUS EUROPEAn MIxES AnD DEnSE-GRADED FRICTIOn COURSES

It is well known that the implementation of contractor quality control/agency quality assurance (QC/QA) can support quality improvements in hot mix asphalt (HMA) pavements, both for porous European mixes (PEMs) and dense-graded friction courses (DGFCs). On the other hand, many reasons and reports highlight the importance of proper in situ air voids content, due to major influence on service properties (rate of rutting, fatigue life, structural strength, permeability, ravelling, etc.). Another relevant standpoint is that in-lab determinations of density, though often reliable and accurate, are low-speed tests. All these facts outline the potential role of field measurement of density through non-nuclear density gauges. In the light of the above facts, the main object of the paper was confined as the study of factors affecting variance and bias of non-nuclear density gauges both for PEMs and DGFCs. Bias, variance and parameters’ dependence resulted to be appreciably affected by mix typology and characteristics. In particular, when related to mix type, monovariate regressions with low-speed methods resulted able to provide a useful tool in QC/QA procedures and road asset management. Further practical applications have been outlined.


Problem statement
Quality assurance (QA) programs have an outstanding importance to ensure that materials and procedures are satisfactory for obtaining adequate life cycle performance (Burati et al. 2003;Kashevskaya 2007;Petkevičius, Christauskas 2006;. On the other hand, the link between pavement insitu density (as quality measure) and service life is assessed both on a theoretical and experimental point of view (Brown et al. 2004;Harrigan 2002;Kennedy et al. 1990;Poulikakos et al. 2004). According to many contracts, in situ density (measured on cores) must be at least 95-97% of the laboratory density obtained, for example, through gyratory (100 gyrations for DGFCs or 50 gyrations for PEMs) or Marshall compaction (75 blows per face -DGFCs or 50 blows per face -PEMs).
Similarly, in other contracts (Spellerberg, Savage 2004), the relative density (bulk on max specific gravity) is the key-factor in judging the performance and in controlling the constructions of HMA pavements. In-lab determinations of density (dimensional, parafilm, vacuum sealing, saturated surface dry, etc), though often reliable and accurate, when applicable, present the drawback of low-speed surveys. In the light of the above facts, many research and technological efforts have been directed to nuclear and non-nuclear portable devices. In particular, non-nuclear density gauges (constant voltage, electrical impedance approach) have been evaluated under many projects (Kvasnak et al. 2007).
As far as non-nuclear devices are used to assess HMA courses quality, more specific problems arise. Some of them relate to the problem of measurement reliability in the case of open graded mixtures (such as the PEMs), or dense graded (such as the DGFCs), and therefore to the metrological performance in a very large range of densities (from 1.9 g/cm 3 up to 2.4 g/cm 3 ). Another issue is a possible deflection or modification of the electromagnetic field due to micro-layers of water beneath the surface layer or due to temperature effects. Moreover, a probable alteration of the electromagnetic field could be associated with the open structure of PEMs.
In the light of the above facts, the main object of the paper was confined to the study of factors affecting variance and bias both for PEMs and DGFCs.
Next section addresses the design of experiments, while in section 3 results are reported and discussed.

Experimental plan
In the design of experiments, the project selection was based on mix design and pavement design factors and consisted of 3 projects, some of which entailed multiple paving days but the same job mix formulas.
As a consequence, this made up 3 different mix designs, of which 2 mix designs involving paving over 2 days.
In order to pursue the above-mentioned objectives, the following main variables have been considered in the project: densities P J (g/cm 3 ): density measured by a portable non-nuclear density gauge, where J = U stands for un-clustered, J = CE for central, and J = CL, for clustered, i.e. as average of 5 cluster points, 1 at the centre, and 4 at corner points (Kvasnak et al. 2007); core specific gravities, G mb (dimensionless, g/g): G mbdim (dimensional method), G mbpar (parafilm method), G mbcor (vacuum sealing method), estimated according to the algorithms and standards specified in Table 1. In the dimensional method, the volume is based on height and diameter/width measurements. Surface irregularities (i.e. the rough surface texture of a typical specimen) introduce inaccuracy. Parafilm method determines the volume according to the water displacement principle but uses a thin paraffin film to wrap the specimen. However, in practice, the film application may be quite difficult and test results can be inconsistent.
Vacuum sealing method (VSD) calculates specimen volume like the parafilm method but uses a vacuum chamber to shrink-wrap the specimen in a high-quality plastic bag.
Note that all the cores have been extracted from the location CE above-mentioned: W  , i.e. sieve size one size larger than the 1 st sieve to retain more than 10% of the material. Two NMASs have been considered: 10 mm, 19 mm. The reference density measurements used were the density measurements from cores. Reasons for this rely on the importance of cores density in European contracts. Further, it is important to remark that many studies confirm that G mbcor results the most reliable among the three considered methods (Cooley et al. 2002;Crouch et al. 2003).

ASTM D 6752
Note: A -mass of the dry specimen in air; abs > 2%: absorption more than 2%; B -mass of saturated-surface-dry specimen in air; B' -mass of dry and sealed specimen; C -mass of HMA sample in water; D' -mass of the dry, coated specimen; E' -mass of sealed/coated specimen under water; F -specific gravity of the coating determined at 25°C; F p -specific gravity of the paraffin at 25°C; F t -apparent specific gravity of plastic bag; G mb -bulk specific gravity; V Geom -geometric volume of HMA sample; VSD -vacuum sealing device; γ w -density of water.

Results
Tables 2-6 and Figs 1-16 summarize the obtained results. In Table 2 the main statistics (average, standard deviation, coefficient of variation CV) of the dependent (P J ) and independent (T, T OA , W OA , γ g , NMAS, WI) variables are provided, together with G mbcor .
Regarding the main statistics, it is possible to say that when G mbcor increases (i.e. in the transition from PEMs to DGFCs), generally P J (in particular P CE ) increase in terms of averages, standard deviations and coefficients of variation, while aggregate specific gravities decrease, due to the fact that, for the selected projects, the design aggregate source was basalt (igneous rock) for PEMs and limestone (sedimentary rock) for DGFCs. Similarly, when G mbcor increases, NMAS decreases, due to the fact that the for the selected projects, NMAS was 19 mm for PEMs (thickness of the layer 50 mm ca.) and 10 mm for DGFCs (thickness of the layer 30 mm ca.). Averages range from 1.8 g/cm 3 (very open PEMs) up to 2.2 g/cm 3 (DGFCs).
Water content (W) results usually lower for PEMs than for DGFCs. Though the appreciable variance, this fact could be related to the different characteristics of water dispersion between PEMs (high) and DGFCs (low).

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Of course, meteorological parameters (T OA , W OA , W) confirm independence from mix type.
Moreover, both for PEMs and DGFCs, G mbcor is usually higher than P CE (3∼4%, Fig. 1 and Table 2). The coefficient of variation of P CE is lower than that of G mbcor for PEMs, while it has an appreciable increase for DGFCs. Table 3 and Figs 2, 3 show the R-square values obtained in the case of monovariate correlations, while in Figs 4-9 main scatter plots are reported (the dotted line in Fig. 4 refers to the line of equality).   Regarding the correlations of P J (i.e. P CE or P CL ) and each of the remaining variables (G mb , W, T, WOA, WI, TOA, γ g , NMAS), it is possible to say that (Figs 2-9): the following main dependences can be considered very significant: P CL (or P CE ) vs. G mb (Table 3 and Fig. 4), P CL (or P CE ) vs. W (Table 3 and (Fig. 3). Such experimental evidences support the importance of daily calibrations, especially for PEMs. On the contrary, as far as more days, more lots are considered for PEMs, there is an improvement of density gauge performance (Fig. 2). Note that in general density gauge performance for DGFCs don't result dayspecific (Figs 2, 3); as for R-square values among "independent" variables (W, W OA , WI, T OA , γ g ) it is possible to point out that they are usually uncorrelated. 3 exceptions can be listed: T vs. T OA (due to the intrinsic meaning of T and T OA ); NMAS vs. W (the lower NMAS, the higher W, probably due to an increased aptitude to detect surface phenomena and/or to high moisture contents for DGFCs); NMAS vs. γ g . In − − − − − particular, Fig. 8, in which P CE is compared to aggregate specific gravity, shows that for the selected sections of the project PEMs mixes had frequently high quality aggregates; dependence on W results to be day-specific both for PEMs and DGFCs, but this phenomenon is more evident for PEMs (Fig. 3); this fact could be the reason for the consequent day-specificity of relationships P J -G mb (Fig. 2). The level of significance of correlations (all the mixes, p-values) is summarized in Table 4. The value reported in it 4 represents the probability of making the "wrong decision", i.e. a decision to reject the null hypothesis (the 2 variables are not correlated), when the null hypothesis is actually true (Type I error, or "false positive determination"). The smaller the p-value, the more significant the result is said to be. It is confirmed that: the "P CE vs. G mb " correlations are significant (at a 1% level of significance); T, WI, W OA and T OA are, in general, low significant for P CE ; the P CE vs. W correlation is significant at a 1% level of significance.
Figs 10-15 refer to the coefficients obtained for the linear regressions involving P CE . It is possible to observe that the coefficient a represents the 1 st derivative and is intrinsically related to the R-square value, the coefficient b represents the value of P CE if the water content (or G mb ) approaches the 0, i.e. if it becomes negligible. As far as P CE and P CL correlations with cores specific gravities are concerned, coefficients a i and b i results are quite similar (for this reason only P CE coefficients are reported in the plots). Note that the higher the reference density (G mbcor ), the higher the variance and the coefficient of variation of P CE (as above-observed in Table 2), the lower the constant (b) of the relationship P CE vs. W (Figs 10 and 12), the higher the 1 st derivative a of the relationship P CE vs. W (Figs 10  and 13), the stronger the dependence on water content (W, Fig. 14) and, of course, the stronger the correlation with the effective density (Fig. 15). Table 4. Correlation significance (all the mixes)    The significance of such behaviour could rely in better performance (both for W and P measurement) as far as denser mixes (influence of mix typology) and "surface/ interface" properties are concerned, probably due to the distribution of the electromagnetic field in the layer. Figs 14, 15 provide a synthesis of this issue. Tables 5, 6 show monovariate and multivariate Rsquare values for each of the considered monovariate and multivariate models. Only linear equations have been considered. α, β, λ, μ and ε have been determined according to the least square method for each of the considered specific gravity (G mbdim , G mbcor , G mbpar ). As far as multivariate correlations between P CE and G mb are concerned (Table 6), it is possible to point out that the augmentation of R-square values due to the consideration of 1 or 2 additional independent variables (W or W and T) ranges from 5% up to 13% in terms of explained variance.  Fig. 16 shows the statistical performance of model (I). It is very interesting to observe that it is (model I Table 5):

Conclusions
It is well-known that high-speed, high precision, security and safety are key factors in QA/QC procedures and strategies.
In a context in which dense-graded and open-graded HMA courses do coexist, non-nuclear portable density gauges could be the answer to many contractor-agency controversies.
Putting at work new procedures in the aim to obtain better performance and lower costs still remains a challenge.
In the light of the obtained results the following conclusions can be drawn. 1. P J values are greatly affected by water content. This fact can be crucial due to seasonal variations and calls for a better analysis and measurement of pavement moisture. 2. The interface between the gauge and the tested HMA layer is of primary importance: the denser and the dryer it is, the lower the bias, the better the correlation with reference core densities. 3. Mix type affects regressions coefficients and biases: the denser the mix, the better the performance even if the higher the dependence on water content. 4. Mix type, or better, mix density seems to affect greatly the variance of P J as related to the variance of reference density (G mbcor , for example): the denser the mix, the higher the variance. This fact could depend on the high sensitivity to the state of the surface layer. 5. Pavement temperature did not result in consistently affect density gauge performance. As a practical application that is relevant to QC/QA procedures it is interesting to observe that at the end of each day the ratio P CE /G mbcor ranged from 1.02 up to 1.06 for PEMs and from 0.99 up to 1.05 for DGFCs.
Future research will aim to address a better understanding of the above-mentioned phenomena and their consequences on contractor and agency risks, through the consideration for other mix types and through the optimization of the experimental plan.